Probing high scale SUSY in low energy FCNC Kei Yamamoto （Niigata Univ. ⇒ KEK from this April） Seminar @ Hiroshima Univ. 2015 Mar. 18 Collaborated with Morimitsu Tanimoto (Niigata Univ.) arXiv: 1503.XXXX

Standard model has been established? ・Higgs discovery [PDG 2014] [CMS 1309.0721] 質量と結合の関係 If　SM　Higgs,Source　for　all　particlesʼmass: coupling/mass　=　VEV　(const.) m_H SM content Mass VS. yukawa

Standard model has been established? Flavor side SM explains CP violation of K and B mesons successfully ⇒ see briefly Also, no signals of lepton flavor We examine the sensitivity of High Scale SUSY in the CP violations of K and B mesons

CP violation CP symmetry : Symmetry between particle and antiparticle C (charge) transformation P (parity) transformation CP symmetry is violated CP violation have been observed in K and B mesons decays. These neutral mesons oscillate between particle and antiparticle. Box diagram of Neutral meson mixing

CP violation CP asymmetry If CP symmetry is conserved, the decay rate of neutral meson and should be equal. 2 CP violation : mixing : decay f : CP conjugate state CP asymmetry CP violation

CP violation in SM CKM matrix フレーバー固有状態と質量固有状態のずれ フレーバーを変える Mass eigenstate basis CKM matrix (wolfenstein parametrization, λ(Cabbibo angle)~0.2) Deviation between flavor eigenstate and mass eigenstate　⇒　change flavor One complex phase　⇒　induce CP violation フレーバー固有状態と質量固有状態のずれ　 フレーバーを変える 1つの複素位相　　CP対称性を破れを引き起こす

CP violation in SM CKM matrix The unitarity triangle Unitarity ： Bs meson system（s-b system） K meson system（d-s system） UT6つ B meson system（d-b system） Im Re 三辺が同オーダーのB中間子系が最も見やすい（Imが大きい）

CP violation in SM CKM matrix The unitarity triangle These angles and lines of UT are determined by various measurements of B and K meson ⇒ Belle, Babar,, Unitarity ： The unitarity triangle Bs meson system（s-b system） K meson system（d-s system） UT6つ B meson system（d-b system） Im Re 三辺が同オーダーのB中間子系が最も見やすい（Imが大きい）

Standard model has been established? SM explains CP violation of K and B mesons successfully No significant deviation, but - a number of tensions - future measurements can improve a lot New Physics contributions to loop processes are still possible Also, no signals of lepton flavor We examine the sensitivity of High Scale SUSY in the CP violations of K and B mesons

Physics beyond SM We need new physics(NP) beyond SM Neutrino oscillations Dark matter（25% of the Universe） Dark energy Baryon asymmetry of universe Hierarchy problem あるはず　示唆 Gauge symmetryから出てくものではない　（color, charge はsymmetry） We need new physics(NP) beyond SM ・大統一理論 ・暗黒物質の存在 ・宇宙のバリオン数非対称性 ・ニュートリノ質量 ・階層性問題 ・…

Example of NP : Supersymmetry (SUSY) Symmetry between fermion and boson Spin 0 Spin 1/2 Spin 1/2 Spin 1 Spin 0 Spin 1/2 assuming no CP violation in the Higgs potential, lighter and heavier CP-even Higgs bosons (denoted as h and H, respectively), CP-odd (pseudo-scalar) Higgs A, and charged Higgs H± Squark Slepton Gluino Bino Wino Higgsino Neutralino Chargino } 2HDM 19 8 レプトン スクォーク S- Spin 1 / 2 0 グルイーノ - ino Spin 1 1 / 2

How to search NP Direct search (e.g. ATLAS, CMS) @ High energy Produce new particle directly with high energy collider High Energy Indirect search (e.g. LHCb, Belle) @ Low energy Probe the effect NP in low energy physics induced by quantum correction Low Energy

How to search NP ⇒ Indirect search for NP is important Direct search (e.g. ATLAS, CMS) @ High energy Produce new particle directly with high energy collider High Energy There are no evidence for new physics Indirect search (e.g. LHCb, Belle) @ Low energy Probe the effect NP in low energy physics induced by quantum correction Low Energy ⇒　Indirect search for NP is important

How to search NP indirectly １：See processes forbidden or suppressed in SM ・　Rare decay、CPV ・　μ→ｅγ、τ→μγ、τ→ｅγ、 ・　Electric magnetic moment（EDM）　de、dN ・　Proton decay 2：Precise measurement ・　Lepton universality ・　（g−2）μ ・　EW precision test Flavor physics 王道2：精密測定による標準模型との差

How to search NP indirectly １：See processes forbidden or suppressed in SM ・　Rare decay、CPV ・　μ→ｅγ、τ→μγ、τ→ｅγ、 ・　Electric magnetic moment（EDM）　de、dN ・　Proton decay 2：Precise measurement ・　Lepton universality ・　（g−2）μ ・　EW precision test Flavor physics

Progress of B physics measurements The LHCb collaboration has reported new data of the CP violation of Bs meson. Time dependent CP asymmetry in βs UT @ Bs SM consistent NPが強く制限される Experimental situations This is the first measurement of the CP violating phase in the Bs->phiphi decay. ----- 会議メモ (2015/03/16 17:07) ----- LHCbのスライドを入れる Exp. [LHCb@1fb-1, 1304.2600] SM [The CKMfitter,2011] Time dependent CP asymmetry in Exp. [LHCb@3fb-1, 1407.2222] SM [M. Bartsch et al.. 0810.0249]

Progress of B physics measurements Rare decay of Bs meson In SM, 　　- loop suppressed - CKM suppressed :BR |Vtb*Vtq|2　 - helicity suppressed :BR mμ2/mBs2 BsはPseudoscalar -> no photon penguin CPSはCPとCSの線形和 ⇒ Rare decay：BR(Bs→μμ)SM 〜 10-9 BR(B→μμ)SM 〜 10−10

Progress of B physics measurements Rare decay of Bs meson [Bobeth et al.1311.0903] [LHCb+CMS] SM consistent BsはPseudoscalar -> no photon penguin CPSはCPとCSの線形和

Progress of B physics measurements Rare decay of Bs meson New data of CP violation of Bs are consistent with SM. [Bobeth et al.1311.0903] ⇒　Constrain to NP [LHCb+CMS] SM consistent BsはPseudoscalar -> no photon penguin CPSはCPとCSの線形和

ＮＰへの感度 Sensitivity to NP Loop process SM loop suppressed CKM suppressed NP ----- 会議メモ (2014/12/06 14:36) ----- シンプルに　KMのようなフレーバー抑制がないとすれば It has sensitivity to high scale NP

Sensitivity to NP NP Neutral meson mixing SM NP model depend ----- 会議メモ (2014/12/06 14:36) ----- シンプルに　KMのようなフレーバー抑制がないとすれば

Effective Theory By integrating out heavy particle which mediate, B transition is described in terms of interaction between light particles. ex) b → cud - Searching for SUSY particle at LHC b c - d u W b c d - u g Intermediate state Transision amplitude Dim.6 quark operator , which is expressed in terms of initial and final state quarks. Wilson coefficient Dim.6 Local operator

49 9 Effective Theory By integrating out heavy particle which mediate, B transition is described in terms of interaction between light particles. ex) b → cud - Searching for SUSY particle at LHC b c - d u W b c d - u g Wilson coefficients have both contributions, SM and New physics. Dim.6 quark operator Wilson coefficient Dim.6 Local operator

Effective Hamiltonian Effective Theory Effective Hamiltonian Ex) i : index of mode Decay amplitude Hadronic matrix element

SUSY search and Flavor physics No evidence of SUSY, and SUSY scale may be much higher than 1 TeV Indirect Search for SUSY is needed ⇒　Flavor physics Our motivation We examine the sensitivity of High Scale SUSY in the CP violations of K and B mesons Flavor physics　 ⇔　 SUSY search by LHC CP asymmetry in B0 meson Time dependent CP asymmetry Semileptonic CP asymmetry εK (CPV of K meson) Kaon rare decay Neutron EDM High scale SUSY SUSY is not observed -> Indirect search by B and K decays It is known epsilonK is poweful in 10 TeV scale. wolfgang figure (rough estimate) mass eigen state epsilonK is powerful at collerate to K to pinunu ~ mq , mg = 10 TeV & 50 TeV KL→ π0νν εK K+→ π+νν

Contents SUSY setup Squark flavor mixing Squark mass spectrum Numerical analysis CP asymmetry in B meson decays chrome EDM of the strange quark εK and Kaon rare decay ←new

Contents SUSY setup Squark flavor mixing Squark mass spectrum Numerical analysis CP asymmetry in B meson decays chrome EDM of the strange quark εK and Kaon rare decay ←new

超対称標準模型でのCP対称性の破れ Squark flavor mixing ：complex The origin of flavor violation SM：The off diagonal elements in the CKM matrix MSSM：The off diagonal elements in the squark mass matrices ↑ It contains the new CP-violating phase 　　　　　　　　：complex 　　⇒ new CP violating phase ※クォーク質量行列と同時対角化できるとは限らないので非対角成分が残る ほぼうまく説明できている

Squark flavor mixing The origin of flavor violation Horyuu The soft squark mass matrices contain the CP-violating phases, which contribute to the flavor changing neutral current (FCNC) with the CP violation. Squark flavor mixing The origin of flavor violation SM：The off diagonal elements in the CKM matrix MSSM：The off diagonal elements in the squark mass matrices ↑ It contains the new CP-violating phase We work in the basis of mass eigenstate. Mixing matrix it is same at slepton case 30sで M: super CKM basis X parameter new phase apear ※ 1st and 2nd family squarks are degenerate: s12=0 The magnitude of mixing parameters sij ⇨ The magnitude of the SUSY contributions

Squark flavor mixing Mass difference SM SUSY Quark squark Gluino interaction

Squark mass spectrum Λ Q0 mH We should consider SUSY particle spectrum, which is consistent with Higgs Discovery. [M.Tanimoto and KY (2014)] Λ SUSY breaking scale Λ = 1017GeV, 1016GeV Taking universal soft parameters at SUSY breaking scale Λ Running soft masses in SUSY H1, H2 Q0 Lighter CP even higgs besom SM Higgs Comment : not Minimal SUGRA We forgive 10% off diagonal element Gauge mediationだと分かれない SM-SUSY matching scale Q0 =10, 50 TeV Running Higgs coupling in SM λ, m2 HSM mH SM scale mH, 126 GeV

RGE running result @Q0=10TeV dL,R, sL,R bR bL gluino H1 tR H2

Parameter squark and gaunino mass mixing parameters 11 5 mg 〜 mq ~ m3 = mq ~ Parameter squark and gaunino mass [M.Tanimoto and KY (2014)] ※ 6:2:1 Chargino :wino & higgsino Neutralino :wino & bino stop mass(hutatu), sbottom mass, gaugino mass MFV では出てこないことは知られている ので non-minimal FV でやります ----- 会議メモ (2015/03/08 14:58) ----- mass はこうしました mixing ----- 会議メモ (2015/03/08 16:27) ----- M_1 M_2 M_3 bino wino ----- 会議メモ (2015/03/16 17:02) ----- 本来ならckmによってdelta決まるはずだが、今　10％くらいフリーにしている mixing parameters ：free parameter For simplicity, random [Delgado, Garcia, Quiros, PRD90(2014)015016] tanβ and L-R mixing angle : mq [TeV] 10 50 tanβ 10 4.5 ~ Xt θd θu case1 : 0.5 case2 : λ (Cabibbo angle)

Parameter squark and gaunino mass tanβ and L-R mixing angle : mg 〜 mq 11 5 mg 〜 mq ~ m3 = mq ~ Parameter squark and gaunino mass [M.Tanimoto and KY (2014)] 6:2:1 Chargino :wino & higgsino Neutralino :wino & bino stop mass(hutatu), sbottom mass, gaugino mass MFV では出てこないことは知られている ので non-minimal FV でやります ----- 会議メモ (2015/03/08 14:58) ----- mass はこうしました mixing ----- 会議メモ (2015/03/08 16:27) ----- M_1 M_2 M_3 bino wino ----- 会議メモ (2015/03/16 17:02) ----- 本来ならckmによってdelta決まるはずだが、今　10％くらいフリーにしている ※ [Delgado, Garcia, Quiros, PRD90(2014)015016] tanβ and L-R mixing angle : mq [TeV] 10 50 tanβ 10 4.5 ~ Xt θd θu case1 : 0.5 case2 : λ (Cabibbo angle)

Parameter

Parameter LR mixing angle mixing parameters 10TeV 50TeV θd θu θe 0.0061 0.0023 0.0137 0.00093 0.00070 0.00056 mixing parameters ：free parameter For simplicity, random

Contents SUSY setup Squark flavor mixing Squark mass spectrum Numerical analysis CP asymmetry in B meson decays chrome EDM of the strange quark εK and Kaon rare decay

Meson mixing & Time dependent CP asymmetry ΔF=2 process The gluino-sbottom-quark interaction Meson mixing & Time dependent CP asymmetry K-K, B-B , Bs-Bs mixing: ― Standard model + observed value is very sensitive, so it becomes a severe constraint. Time dependent CP asymmetry : SM + SUSY The cEDM of the strange quark $d_{s}^C$ is given in terms of the gluino-sbottom-quark interactions as seen in Appendix C. The upper bound of the cEDM of the strange quark is given by the experimental upper bound of the neutron EDM as

ΔMB /ΔMB ΔMBs /ΔMBs Sin(2Φs)SUSY/Sin(2Φs)SUSY+SM We scan δij randomly in the region of 0　～ 0.5 We scan sij randomly in the region of 0 ～ 0.5 with taking |sijL|= |sijR| ΔMB /ΔMB SUSY SUSY+SM ΔMBs /ΔMBs SUSY SUSY+SM 6% 0.4% S13 S23 Sin(2Φ1)SUSY/Sin(2Φ1)SUSY+SM Sin(2Φs)SUSY/Sin(2Φs)SUSY+SM φ1=β 8% 6% small ----- 会議メモ (2015/03/16 17:02) ----- maximam にとってもBには効かない S13 S23

εK /εK SUSY SUSY+SM 40% sensitive S13S23 We scan δij randomly in the region of 0　～ 0.5 SM component Taking account of Gluino squark interaction ⇒

Time dependent CP asymmetry SM prediction Both CP violations come from CP phase in the mixing. SUSY contribution [S. Khalil ,E. Kou(2003), A.L. Kagan(2002), M.Endo,S.Mishima,M.Yamaguchi (2005)] depends on S23 Difference of sign comes from parity of final state Experimental results [HFAG,2012]

C8g/C8g Time dependent CP asymmetry SηK vs. SΦK SΦK/Sη’K 0.2% S23 S23 SM Our predictions SηK vs. SΦK Time dependent CP asymmetry C8g/C8g SUSY SM SΦK/Sη’K 0.2% S23 S23 insensitive… Q0=10 TeV tanβ=10

Semi-leptonic CP asymmetry CP asymmetry in the semileptonic decay in mixing SM + SUSY Experimental results [LHCb 2012 06] SM predictions Experimental results [PDG 2012] [A.Lenz and U.Nierste, arXiv:1102.4274 [hep -ph]] fomula depend on , depend on

asl asl vs. asl Semi-leptonic CP asymmetry d Semi-leptonic CP asymmetry asl vs. asl s d Our predictions SM asld < 1×10-3, 　asls < 5 × 10-5 insensitive…

Chromo-EDM of strange quark Q0=50 TeV tanβ=3 Chromo-EDM of strange quark [K.Fuyuto, J.Hisano and N.Nagata, 2013] |dsC|< 4 × 10-25 cm Phase 構造の違いで、εが小さくてもedmは大九九なり得る sensitive Upper bound S23 45

Chromo-EDM of strange quark vs. εK Q0=50 TeV tanβ=3 Chromo-EDM of strange quark vs. εK Phase 構造の違いで、εが小さくてもedmは大九九なり得る 46

Chromo-EDM of strange quark vs. εK Q0=10TeV ➡　Q0=50TeV @ Q0=50TeV 二桁実験バウンドより小さい Edmはleft right mixing is supressed large mass def. Order supressed Esilonl is not supressed because it is insensitive left-right mixing ----- 会議メモ (2015/03/16 17:07) ----- edmよりepsilonのほうがよく効くよ 47

Contents SUSY setup Squark flavor mixing Squark mass spectrum Numerical analysis CP asymmetry in B meson decays chrome EDM of the strange quark εK and Kaon rare decay

⇒ Sensitive to New Physics KL → π0νν and K+ → π+νν Rare decay : BRSM 〜10-11 Clean theoretically : theoretical uncertainty 〜2％ [Buras et all, 2006] 理論的不定性が小さい Forn factorがよくわかっている ----- 会議メモ (2015/03/07 18:39) ----- rare decay of k meson decay is powerful NP probe. One example is K to pinunu decay KL topi0nunu is CP violatog decay ----- 会議メモ (2015/03/08 14:57) ----- prove のみ ----- 会議メモ (2015/03/16 17:07) ----- kotoのスライド ⇒ Sensitive to New Physics

K → πνν in SM KL→ π0νν K+→ π+νν Direct CPV K to pinunu Relation 理論的不定性が小さい Forn factorがよくわかっている ----- 会議メモ (2015/03/07 18:43) ----- pure imaginaly part neglecting CPV KK mixing K^+ CP conserve K+→ π+νν K to pinunu Relation Direct CPV Hadronic matrix element, isospin relation K to pinunu deference

K → πνν in SM η ρ K+→ π+νν KL→ π0νν KL→ π0νν K+→ π+νν Direct CPV Future (20XX) CP - CP + KL→ π0νν Direct CPV 理論的不定性が小さい Forn factorがよくわかっている ----- 会議メモ (2015/03/07 18:43) ----- height K+→ π+νν K to pinunu Relation Hadronic matrix element, isospin relation K to pinunu deference

⇒ Sensitive to New Physics KL → π0νν and K+ → π+νν Rare decay : BRSM 〜10-11 Clean theoretically : theoretical uncertainty 〜2％ [Buras et all, 2006] 理論的不定性が小さい Forn factorがよくわかっている ----- 会議メモ (2015/03/07 18:39) ----- rare decay of k meson decay is powerful NP probe. One example is K to pinunu decay KL topi0nunu is CP violatog decay ----- 会議メモ (2015/03/08 14:57) ----- prove のみ ----- 会議メモ (2015/03/16 17:07) ----- kotoのスライド ⇒ Sensitive to New Physics Experiment ←KOTO experiment @J-PARC

[yamanaka, Flavor in new physics @ J-PARC (2015) ]

[yamanaka, Flavor in new physics @ J-PARC (2015) ]

K → πνν and εK in MSSM MSSM MSSM It is known there are no large enhancement in K → πνν decay in the Minimal flavor violation(MFV) scheme SUGRA model with MFV [T.Goto, Y,Okada and Y.Shimizu(1998)] @ Squark mass < 600 GeV, Gaugino mass < 600 GeV with non-MFV [A.J.Buras,et al (2005)] @ Squark mass = 600 GeV, Gluino mass = 1 TeV, δ13, δ23 ~ 0.3 Goto: SUGRA and Minimal flavor violation(universal soft parameter) 小さい 数％、susy region 書く MFV: the flavor and CP violation are governed by the CKM matrix, the so-called MFV MSSM MSSM It is known there are no large enhancement in K → πνν decay in the Minimal flavor violation(MFV) scheme

K → πνν and εK in MSSM In the MSSM SM exchange exchange exchange Dominant term comes from 長い chargino + gluino 1

Numerical analysis results @ Q0=10 TeV K→πνν : Chargino dominant εK : Gluino dominant epsilon_K constraint chargino contribution in the unit of the SM

Numerical analysis results @ Q0=10 TeV @sd=su=0.1 with 90%C.L. |εK|exp constraint Grossman-Nir bound 〜 8 × SM 〜 3 × SM SM 1σ exp. bound @sd=su=0.1 @sd=0, su=0.1 ----- 会議メモ (2015/03/07 19:02) ----- epsilon_K constraint at most 30% at most 3%

Numerical analysis results @ Q0=10 TeV sd & su dependense 〜 100 × SM 〜 20 × SM 1σ exp. bound ----- 会議メモ (2015/03/07 19:09) ----- ＊K+に実験値のライン入れる

Numerical analysis results @ Q0=50 TeV @sd=su=0.3 Grossman-Nir bound 〜 2 × SM 〜 2 × SM SM 1σ exp. bound @sd=su=0.3 @sd=0, su=0.3 at most 10% at most 1.5%

Summary We have studied the contribution of the high-scale SUSY to B and K meson systems We consider the high-scale SUSY at 10-50 TeV scale in the framework of the mass eigenstate basis of the SUSY particles assuming the non-minimal squark (slepton) flavor mixing As results, is most sensitive even if the SUSY scale is higher than 50 TeV Chrome EDM has a sensitivity at SUSY scale 10-50TeV CP asymmetry and mass difference of B meson are insensitive to high scale SUSY To prove the high scale SUSY We also assume that AX , MgX , and mu are all real parameters to avoid a large electric dipole mo- ment of the neutron If large NP contribution to both and come out, it may suggest the contribution of chargino and gluino are comparable. Even if the NP contribution to is small, can be enhanced. We expect the measurement of these processes will be improved by the J-PARC KOTO experiment (and CERN NA62 experiment) in the near future.

Summary Intensity frontier is crucial to probe BSM ! [Iijima, Flavor of new physics @ J-PARC (2015) ]